Atlanta — The tea party got a big win in Nebraska's GOP Senate primary on Tuesday, but whether it can duplicate that in next week's GOP race for the open Senate seat in Georgia – the heart of tea party country – looks dubious.

Two tea party-themed conservatives in the race – six-term US Rep. Phil Gingrey, an OB/GYN, and four-term US Rep. Paul Broun, an Athens, Ga., doctor – entered the race high in hopes. But a week before Georgia voters head to the polls to choose the nominees, they're back in fourth and fifth places, running behind three "establishment" Republicans and just ahead of "undecided."

Why are the tea party candidates fading in the stretch? Lots of factors are in play, but analysts say the answer comes down to this: The GOP establishment, in a bid to ensure that an electable Republican makes it through to the general election, is fighting back.

Instead, two more-traditional-looking Republicans – millionaire David Perdue, a former Dollar General CEO and a cousin to former Georgia Gov. Sonny Perdue (R), and US Rep. Jack Kingston, a former farm insurance salesman who ran on term limits and has now been in Washington for 21 years – have solid leads in the polls. Another mainstream Republican, former Secretary of State Karen Handle (who nearly won the governorship in 2010) has dared the Democrats to try to peg the “war on women” meme on her campaign as she’s vaulted into third place, according to polls.

“Republicans have had a chance to win the majority [in the Senate] and instead they’re losing,” says Jennifer Duffy, a senior editor at the nonpartisan Cook Report. “Frankly, they’re tired of losing.”

If the poll trends hold and the tea party candidates don’t qualify for an expected runoff, establishment Republicans will have “dodged a more serious bullet” given the piecemeal support spread across so many candidates, says Ms. Duffy. “If a tea party candidate makes the runoff, you’d see the tea party groups coalesce behind one candidate, and it would become a very different race. The objective has been to prevent Broun or Gingrey from making that runoff.”

As happened in Nevada, Delaware, and Indiana in previous election cycles, nominating a firebrand conservative populist with narrow bona fides and quirky views could cause Republicans to lose a key seat in a year when the party is within reach of grabbing the Senate majority.

The GOP establishment's pushback in Georgia started as a mere gear switch in the election machinery: moving Georgia’s primary day up to May 20 – the earliest date ever down here in the 13th original colony. The move was part of a federal judge’s order, to allow more time for military overseas ballots to arrive in case of a July runoff.

But the decision by state GOP officials to agree to the change had an ulterior motive: Sliding up the primary date to a time when kids are still in school and the Georgia vacation season has not started, party insiders hoped, would increase turnout and dilute the clout of tea party vote-casters in the primary, who had yanked the Republican Party hard to the right in the 2010 and 2012 election cycles.

Those developments jibe with an emerging national picture of a tea party movement that, after helping to reinvigorate the Republican Party in the Obama era, has become hobbled by its embrace of flawed or extreme candidates. As the movement’s popularity wobbles, the Republican establishment is working to rebuff tea party insurgents in Georgia and elsewhere. The US Chamber of Commerce, for instance, is helping to fund Representative Kingston’s surging run.

While mainstream Republicans ignored the tea party in 2010 and tried to be friends in 2012, “[i]n 2014 they’re fighting back,” Ms. Duffy told McClatchy Newspapers this week.

Polls and campaign contributions back that up. A new Marist Poll shows a wide gap in Georgia between the moderate GOP frontrunners and the two more-conservative candidates pushing for “liberty and prosperity,” as Representative Broun’s website puts it. Marist Poll director Lee Miringoff draws the conclusion that tea party influence is flagging, in part, because their candidates' war chests pale in comparison to those of the front-runners.

For GOP insiders, the prospect of either Broun or Representative Gingrey advancing to a July runoff is anathema. Though popular among small-town voters in Georgia’s lake country, Broun has called the theory of evolution a “lie from the pits of hell,” and Gingrey, who has assisted on more than 5,000 births, called “partly right” former US Rep. Todd Akin’s 2012 remark that women’s bodies could shut down pregnancies after “legitimate rape.”

Meanwhile, Democrats aren't messing around. Front-runner Michelle Nunn, former Points of Light Foundation CEO and daughter of former Sen. Sam Nunn (D) of Georgia, is campaigning as a rock-solid moderate. According to an Atlanta Journal-Constitution poll released last weekend, she has a good shot to win a race against any of the Republican candidates.

As of Tuesday, statisticians at The New York Times’s Upfront blog rate the Georgia Senate race as “toss-up,” with the newspaper’s Josh Katz saying that designation “is highly contingent on which Republican emerges from the primary next Tuesday.”

According the Times’s statistical model, Ms. Nunn has a 73 percent chance of winning against Gingrey but only a 26 percent chance of beating Perdue.

Though the tea party candidates are flagging in this race, tea partyers' complaints still resonate in Georgia. Georgians disapprove of President Obama – long a tea party foil – by a large margin, and rock-solid majorities here tell pollsters that Washington Democrats are taking the country in the wrong direction.

Moreover, tea party candidates in other states, including Curt Clawson in Florida and Alex Mooney in West Virginia (both House races), have already won their primaries, suggesting that the movement’s struggle in Georgia could be localized.

A sizable share of Georgia voters see Broun and Gingrey as flawed candidates with narrow appeal, says Merle Black, an Emory University professor and author of “The Rise of Southern Republicans.” “The stereotype of a Georgia Republican is the most conservative person someone could imagine, and that’s not necessarily the case,” he says.

More broadly, tea party conservatives in Georgia may be seeing some blowback to their considerable policy successes. Georgia's tea party class of 2010 has forged ahead with its "pro Constitution" policies, focusing on expanding gun rights, introducing Christian shield laws that allow some proprietors to refuse services to gay customers, and attacking Common Core educational standards as “federalizing” Peach State schools.

While all that is going on, Georgia under the Republicans has, post-recession, struggled to live up to its reputation as the economic center of the Deep South, watching as states such as North Carolina and Tennessee challenge its primacy in high-tech, banking, and sports.

Despite the state’s geographic charms, Atlanta’s international reputation, and historically pro-business politics in the legislature, the percentage of Georgians who want to leave the state was ranked as “above average,” according to a recent Gallup poll. That's higher than any of the immediate neighbors of the Empire State of the South.

“Republicans now control everything in Georgia … so increasingly Georgia Republicans are seen as the party of government, and are being increasingly evaluated on their performance in government,” says Professor Black. “That’s a major shift.”

But more central than the establishment-versus-tea-party paradigm, says Black, is the fact that the GOP Senate front-runners – Nunn and Perdue – are both political neophytes. That fact, he adds, “says something about the voters’ assessment of people who have been in office.”